Title: Phase-based Metamorphosis of Diffusion Lesion in Relation to Perfusion Values

in Acute Ischemic Stroke

Running head: Lesion metamorphosis modeling and stroke evolution

Authors: Islem Rekik1,2,3, PhD; Stéphanie Allasonnière3 , PhD; Marie Luby4,5, PhD; Trevor K.

Carpenter1,2, PhD; Joanna M. Wardlaw1,2, MD, FRCR, FMedSci, FRSE, on behalf of the

STIR and VISTA Imaging Investigators*

Affiliations: 1Brain Research Imaging Centre, SINAPSE Collaboration;

2Division of Neuroimaging Sciences, University of Edinburgh, UK;

3CMAP, Ecole Polytechnique, Route de Saclay, 91128 Palaiseau France;

4National Institute of Neurological Disorders and Stroke, National Institutes of Health,

Bethesda, MD, USA

5Seton/UT Southwestern Clinical Research Institute of Austin, Department of Neurology and

Neurotherapeutics, UT Southwestern Medical Center, Austin, TX, USA

Abstract

Examining the dynamics of stroke ischemia is limited by the standard use of 2D-volume or

voxel-based analysis techniques. Recently developed spa- tiotemporal models such as the 4D

metamorphosis model showed promise for capturing ischemia dynamics. We used a 4D

metamorphosis model to evalu- ate acute ischemic stroke lesion morphology from the acute

diffusion-weighted imaging (DWI) to final T2-weighted imaging (T2-w). In 20 representative

patients, we metamorphosed the acute lesion to subacute lesion to final infarct. From the

DWI lesion deformation maps we identified dynamic lesion areas and examined their

association with perfusion values inside and around the lesion edges, blinded to reperfusion

status. We then tested the model in ten independent patients from the STroke Imaging

Repository (STIR). Per- fusion values varied widely between and within patients, and were

similar in contracting and expanding DWI areas in many patients in both datasets. In 25% of

patients, the perfusion values were higher in DWI-contracting than DWI-expanding areas. A

similar wide range of perfusion values and ongoing expansion and contraction of the DWI

lesion were seen subacutely. There was more DWI contraction and less expansion in patients

who received thrombolysis, although with widely ranging perfusion values that did not differ.

4D metamorphosis modeling shows promise as a method to improve use of multimodal

imaging to understand the evolution of acute ischemic tissue towards its fate.

Key words: metamorphosis; ischemic stroke; lesion evolution; diffusion imaging; perfusion

imaging, magnetic resonance imaging; diffusion imaging

1. Introduction

The change in ischemic stroke lesions from acute presentation to final tissue damage is highly

variable between individual patients as seen on magnetic resonance diffusion and perfusion

imaging. Following the occlusion of a cerebral artery, ischemic tissue damage is seen as

hyperintense on diffusion- weighted imaging (DWI) often within a larger area of

hypoperfused at-risk, but potentially reversible tissue ischemia, detectable on perfusion-

weighted imaging (PWI). Thereafter the ischemic tissue may grow or diminish depending on

known and unknown factors. Subsequent growth of the lesion core, considered to be

represented by DWI, is generally attributed to persistently reduced perfusion values around

the core, whereas recovery of ischemic tissue is generally attributed to improvement in

perfusion (Wardlaw, 2010).

Many imaging studies have investigated stroke lesion evolution mainly using 2D lesion

volume or voxel-based analyses, but these may not capture the full spatiotemporal dynamics

of perfusion and diffusion lesions as they may under-sample information about the location,

direction or magnitude of the lesion dynamics in space and time (Rekik et al., 2012).

Recently, we applied 4D shape deformation modeling methods to examine the highly

contracting and expanding areas in DWI and PWI lesions (Rekik et al., 2013, 2014).

Of theses methods, the metamorphosis model (Trouv ́e and Younes, 2005; Younes, 2010;

Rekik et al., 2014) handled both multi-component and solitary lesions and incorporated

image intensity values from different sequences, and demonstrated elegance and accuracy of

deforming the source image into a subsequent image, while tracking, point by point, a) the

image intensity values inside and outside the lesion edges and b) the velocity of lesion defor-

mation between timepoints. Notably, the proposed metamorphosis model in (Rekik et al.,

2014) could follow ischemic stroke lesion change in perfusion weighted imaging from the

acute to final infarct. It enabled to explore the perfusion dynamics in ischemic stroke and

their relation to final T2-w lesion outcome (at ≥1month). However, the role of diffusion

weighted imaging, which is fundamental to understanding stroke dynamics, was overlooked.

In this paper, we aim to investigate diffusion lesion local dynamic changes in relation to

perfusion values in the affected hemisphere.

By applying this model to longitudinal images, the present study aims to: (1) model changes

in the acute ischemic DWI lesion from the acute timepoint into the final infarct lesion, in both

solitary and multi-component lesions; and (2) extract measurements of the most dynamic

parts of the lesion to see the most rapid or largest areas of the DWI lesion

expansion/contraction areas in relation to PWI values and clinical features such as stroke

severity. We tested our model on stroke imaging data acquired in an observational study in

one center (Rivers et al., 2006; Kane et al., 2007) and then validated the model in multicentre

data obtained from STIR (Ali et al., 2007).

2. Materials and Methods

2.1 Patient selection:

Development dataset : We first applied the metamorphosis model to 20 representative patients

from a prospective observational study of MRI in hyperacute stroke.7,8 Patients were first

imaged <6 hours of stroke and represented a typical range of stroke severities (NIHSS,

median = 10, IQR: 6-14), ages (74.9±9.2years), acute DWI lesion volumes (34.6±32.2cm3)

and mean transit time (MTT) volumes (126.6±102.2cm3). None of the 20 patients received rt-

PA treatment, thus they represent the natural history of stroke lesion evolution, including any

effects of spontaneous reperfusion. We included patients who had DWI images at acute

(~5hrs) and subacute (~5±1days) timepoints after stroke, a perfusion mean transit time

(MTT) map at least at the acute timepoint, and T2-w lesion at ≥1month after stroke. All

patients had an MTT lesion at the first timepoint but only 12 had an MTT lesion visible at the

second timepoint. Twelve patients had multi-component DWI/MTT lesions and eight had

solitary lesions.

Exploratory dataset: we selected from STIR9 the first 10 of 290 potential cases with three

MRI scans at acute (<6hrs), subacute (5days) and final (≥1month). The first 10 patients that

met the study criteria (age 59.6±16.4years, median admission NIHSS of 7 (IQR: 5-12)) had

all received standard IV tPA thrombolysis. All had perfusion imaging <6hrs but perfusion

imaging was included per protocol at subacute (5 days).

2.2 MRI Pre-Processing:

We used the MTT perfusion map as it is easily obtained and generally shows the PWI lesion

as large.7,8 The modeling was blind to all clinical data and imaging values. Arterial

recanalization status and collaterals were not taken into account in the modeling as

angiographic data were not available for all patients. STIR exploratory data were processed

identically to the derivation data unless stated otherwise. Full details of image acquisition and

processing were described previously.7,10 We obtained MTT areas from the contralateral

hemisphere by mirror reflection of the MTT lesion to the unaffected hemisphere. For each

patient, we generated relative MTT (rMTT) lesion maps by dividing the value of each lesion

voxel by the mean perfusion value of the contralateral MTT values. The resulting intensity

‘rMTT’ has no unit. An expert radiologist visually checked that tissue swelling did not distort

the DWI lesion boundary.

2.3 Two-image based metamorphosis model:

In our previous work (Rekik et al., 2014), we extended the image-to-image metamorphosis

into a spatiotemporal metamorphosis that exactly fits the baseline image to subsequent

observations in an ordered set I = {I0, I1, . . . , IT } images, which we applied to perfusion data

in acute stroke. This model registers one source image to a target image while estimating two

op- timal evolution paths linking these images: (1) a geometric path encoding the smooth

velocity of the deformation of one image into another, and (2) a photometric path

representing the variation in image intensity. Both paths characterize the dynamics of the

image metamorphosis from the source to the target image in small discrete time and space

intervals.

Basically, a baseline image I 0 morphs under the action of a velocity vector field v t that

advects the scalar intensity field I t (i.e. time-evolving image intensity) Trouve and Younes

(2005). Solving the advection equation with a residual allows to estimate both image intensity

evolution and the velocity at which it moves.

We estimated the optimal metamorphosis path ( I t , vt ) starting at I 0, while constraining it to

smoothly and exactly go through any available intermediate observation, till reaching the

final observation I T. This was achieved through minimizing the following cost functional U

using a standard alternating steepest gradient descent algorithm Rekik et al. (2014):

U ( I , v )=∫0

T

|v t|V2 dt + 1

σ2|dI ( t )dt

+∇ I t . v t|L2

2

dt

σ weighs the trade-off between the deformation smoothness (first term)

and fidelity-to-data (second term). The term ∇ I t . v t represents the spatial variation of the

moving image I t in the direction v t. Furthermore, the moving intensity field I t is defined

under the action of the diffeomorphism (invertible smooth mapping) ϕt on a baseline image I 0

: I t=ϕ t . I 0. We associated to the action ϕ a velocity v that satisfies the flow equation rooted

in the in-vogue large deformation diffeomorphic metric (LDDMM) framework (Trouve,

1998):

{dϕt

dt=v (ϕ t ( x ) ) , t∈[0 ,T ]

ϕ0 ( x )=x

In the present study, we used the estimated velocity vector field v t to estimate the total DWI

lesion deformation map in two phases:

1) In the first phase, we morphed acute (< 6hr) DWI lesion to subacute (∼ 5d) DWI lesion in

20 patients; and

2) In the second phase, we morphed the subacute (∼ 5d) DWI lesion into the final T2-w (≥1

month) in the 12/20 patients with subacute perfusion imaging. Retaining these two distinct

phases, ‘acute to subacute’ and ‘sub- acute to final’, facilitated testing of acute separately

from subacute clinical information against the lesion parameters.

2.4 Extracting highly dynamic regions of DWI lesion:

For both phases, in each patient, we generated a total 3D lesion deformation map, computed

as the squared sum of the estimated speed along the metamorphosis path, and identified

contracting and expanding DWI regions (as the ‘negative’ and ‘positive’ deformation values

respectively) during each phase (Figure 1). In the exploratory dataset (STIR), we were only

able to estimate the acute to subacute phases since subacute perfusion imaging was not

available for all 10 patients. We then automatically thresholded the two total metamorphosis

deformation maps generated for the acute-subacute and subacute-late phases of DWI lesion

evolution to compute the proportion by volume of the total DWI lesion boundary that was

rapidly contracting or expanding for the acute-subacute and subacute-late phases.

2.5 rMTT values relation to DWI lesion dynamics:

For each patient, for both phases, for every rMTT voxel value within the acute perfusion

image we computed the mean amount of DWI lesion contraction or expansion. We then

plotted the acute rMTT values against their corresponding mean DWI contraction or

expansion magnitudes (Figure 2). In most cases, both resulting rMTT distributions were

Gaussian. Therefore, we used Gaussian least squares fit to approximate the relation between

acute rMTT values and the mean amounts of DWI lesion deformation: one for contraction

(purple curve in Figure 2) and one for expansion (pink curve in Figure 2). For phase one, the

Gaussian fitting root-mean-square deviation (RMSE) reached 0.0035 ± 0.0042 for contraction

and 0.006 ± 0.014 for expansion, noting that when the fitting is exact RMSE = 0 (no residuals

or perfect test). For phase two, the data also best fitted a Gaussian distribution (RMSE =

0.0029 ± 0.0032 for contraction and 0.0039 ± 0.0058 for expansion). These Gaussian curves

allowed us to estimate the rMTT values associated with rapidly expanding or contracting

DWI regions– along with a confidence interval around these peak values: the upper bound

represents the mean of the Gaussian curve minus its standard deviation and the lower bound

represents the mean of the Gaussian curve plus its standard deviation.

3. Results

Derivation dataset lesion metamorphosis and perfusion values: acute to subacute phases:

The model showed that the mean rMTT values in areas of DWI expansion across patients

(mean 0.8±0.82SD, maximum 3.18) were similar to mean rMTT values in areas of DWI

contraction (mean 0.74±0.63SD, maximum 2.17), Table 1. In general, the range of rMTT

values in all parts of the DWI lesion boundary was wide such that in most of the 20

derivation dataset patients (15/20), the rMTT values in DWI lesion areas that were

contracting were nearly identical to the values in DWI areas that were expanding (correlation

coefficient r=0.86, p=0.8), shown as the overlap of the red and blue vertical bars in Figure 3.

Only in 5/20 patients (25%) were the blue and red vertical bars distinct, indicating that acute

perfusion was clearly better in areas of DWI contraction than in areas of DWI expansion

(Figure 3). In some patients (7/20 in Figure 3), the red bars extended beyond the blue bars

indicating that perfusion values associated with most rapidly expanding DWI areas

encompassed a wider range of MTT perfusion values than in rapidly contracting DWI areas.

Lesion metamorphosis and perfusion values: subacute to final phase:

A similar general pattern of rMTT values was seen in the 12 patients who had rMTT data

available from the subacute to final phases (~5d to >1month, Table 1, Figure 4). The rMTT

values were very similar in DWI expanding and contracting areas in most patients (r=0.91,

p=0.8). In 3/12 patients (25%), subacute rMTT values in DWI contracting areas were higher

than in DWI lesion expansion areas indicating better perfusion in contracting areas. Table 1

also indicates that a) DWI lesions were still expanding into some areas and regressing in

others and b) perfusion values remain very variable during the subacute to final phase.

DWI dynamic evolution features:

We assessed the proportion of the DWI lesion that highly contracted or expanded at each

phase (Table 1). During both phases, 11/20 (55%) patients had more highly expanding than

contracting areas, although the difference in median volumetric proportions of the DWI

lesion was not significant (p=0.62 for acute-subacute and p=0.13 for subacute-final phases).

Also some DWI lesions continued to expand rapidly in some areas and to contract in others in

quite similar proportions, highlighting the dynamism of acute and subacute stroke lesions

(Table 1).

DWI metamorphosis, perfusion and clinical features:

During the acute-subacute phase, there was no association between acute NIHSS and rMTT

values found in expanding (r=0.11, p=0.63) or contracting (r=0.06, p=0.77) DWI lesion areas.

Similarly, during subacute-final phase, there was no association between admission NIHSS

and rMTT values found in contracting (r=0.007, p=0.99) or expanding (r=-0.021, p=0.95)

DWI lesion areas. We also investigated the association between the proportion of the DWI

lesion volume that was highly contracting or expanding during acute-subacute and subacute-

final phases and various clinical factors (acute NIHSS, acute MTT volume, acute DWI

volume), but found no significant correlations. For all, we obtained: (i) acute-subacute phase:

contraction r=0.082, p=0.731; expansion r=0.258, p=0.271 and (ii) subacute-final phase:

contraction r=0.181, p=0.444; expansion r=0.255, p=0.277.

Evaluation of the model in the exploratory dataset from STIR:

In the 10 STIR9 stroke patients, the rMTT values in contracting or expanding DWI lesion

areas were highly positively correlated (r=0.98, p=0.0001) (Table 1, Figure 5). However, a

larger proportion of the DWI lesion was contracting (median: 4.16% of the acute DWI lesion

volume), and a smaller proportion expanding (median: 1.81% of the acute DW lesion

volume) in the STIR exploratory dataset than in the derivation dataset (median: 3.39%

contracting, median: 4.38% expanding), possibly reflecting the effects of thrombolysis in the

STIR patients.

5. Discussion

We show that a dynamic metamorphosis model (Rekik et al., 2014; Trouve and Younes, 2005;

Younes, 2010) has promise for modeling ischemic stroke lesion evolution using acute and

subacute DWI, rMTT and final T2-w images in space and time. This enabled us to visualize

and extract dynamic features of the ischemic lesion, such as the magnitude of contraction and

expansion of the DWI lesion as a function of lesion volume and in relation to rMTT values.

In our heterogeneous, small, but representative samples, we found that (i) dynamic changes in

the DWI lesion were not confined to the first few hours after stroke but continued for days or

weeks, accompanied by wide-ranging perfusion values; (ii) a similar wide range of perfusion

values were associ- ated with large DWI lesion deformations from acute to subacute

timepoints within individual patients, meaning that in most patients (75%) the rMTT values

covered the same range in contracting and expanding DWI regions; in about 25% of patients

in both datasets, the perfusion values were higher in contracting than expanding DWI

regions; (iii) there was large variation between patients in the perfusion values in DWI lesion

areas that undergo the largest deformations, even where there was greater DWI contraction

af- ter thrombolysis; and (iv) there was large between-patient variation in the amount of DWI

lesion change in acute to final phases after stroke, although we found more DWI lesion

contraction in patients in STIR who received thrombolytic treatment than in the observational

study where no patients received thrombolysis.

Our findings suggest that PWI values are more heterogeneous than has been suggested using

average values obtained from DWI and PWI data obtained from regions of interest at

individual timepoints (Dani et al., 2012). The variation is consistent with the wide variation

in perfusion levels found in the literature (Kane et al., 2007; Dani et al., 2012), and with the

recent concept of perfusion strata (or confidence intervals) as a biologically plausible

representation of infarct risk maps (Nagakane et al., 2012). The absence of a clear difference

between perfusion values in expanding versus contracting DWI lesion areas in 75% of our

small but representative group of 30 patients points to a need to identify other factors that

influence DWI lesion progression or reversal. The influence of lesion swelling, perfusion

heterogeneity at capillary level (Ostergaard et al., 2013), collaterals, completeness of arterial

occlusion at the primary occlusion site (Rekik et al., 2012; Phan et al., 2009) and perfusion

levels assessed with other perfusion parameters, should be examined in future studies.

Since our sample lacked statistical power due to its small size, the method should be applied

in larger datasets of stroke patients with varied lesions, timepoints, treatments and outcomes

and with other perfusion parameters. Although we did not explicitly model the effect of

arterial patency, the per- fusion being delivered to the tissues was captured in the voxel-level

rMTT values. These observations of stroke lesion ‘natural history’ in the 20-patient derivation

dataset and ‘thrombolysis-enhanced’ in the 10 patient exploratory dataset, highlight the

complexity and the variability of ischemic stroke lesion dynamics (Scalzo et al., 2013).

Further refinement of the 4D model and inclusion of other factors such as recanalization and

lesion swelling would further advance our understanding of these dynamics, explain

inconsistencies between past studies Dani et al. (2012), and provide a more nuanced

understanding of how perfusion values influence DWI lesion progression to different fates.

6. Conclusion

In this work, we used the metamorphosis model that tracks both intensity and shape changes

in evolving images to examine the influence of local voxel- wise perfusion values on

ischemic lesion core dynamics (i.e. contraction and expansion) visible on diffusion weighted

imaging. The wide range of perfusion values and lack of difference between contracting and

expanding areas emphasizes the very dynamic nature of stroke and explains difficulty in

using threshold values to discriminate tissues states. Indeed, the noted observations add up to

the growing evidence of the wide spectrum of heterogeneous perfusion values, and question

the true extent of their contribution into determining final infarcted tissue boundary. As noted

in (Rekik et al., 2012), we believe that applying highly advanced, accurate and robust medical

image analysis methods will help neurologists and stroke researchers converge to a unified

vision of stroke dynamics and what truly drives tissue death. More clinical factors remain

broadly unknown and others can be included into honing these models in future studies (e.g.,

swelling or spontaneous reperfusion). Patient-specific dynamic modeling could be of

potential use in future larger studies to determine what factors influence stroke lesion

evolution and responses to treatment in individual patients. Such advances are necessary to

determine in future which patients are most suited to which treatments – i.e. personalized

medicine.

Sources of Funding:

This study was funded by the Scottish Funding Council through the Scottish Imaging

Network, A Platform for Scientific Excellence (SINAPSE) Collaboration

(http://www.sinapse.ac.uk/), the Centre for Clinical Brain Sciences, the Tony Watson Bequest

and a Scottish Overseas Research Award from the University of Edinburgh (PhD for Islem

Rekik), the Scottish Funding Council SINAPSE Collaboration (to Prof. Joanna Wardlaw), the

Cohen Charitable Trust (to Dr. Trevor Carpenter and Dr Islem Rekik), and the Chief Scientist

Office of the Scottish Government.

This work was also supported by Seton/UT Southwestern Clinical Research Institute of

Austin, Department of Neurology and Neurotherapeutics, UT Southwestern Medical Center,

Austin, TX, USA and the National Institute of Neurological Disorders and Stroke (NINDS),

National Institutes of Health (NIH), Bethesda, MD, USA.

Disclosure/Conflict of Interest

The authors declare no conflict of interest.

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Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure legends

Figure 1. (a) Axial images of acute MTT (left), acute DWI (middle) and subacute DWI

(right). (b) Axial images of subacute MTT image (left), subacute DWI image (middle) and

final T2-w image (right). During acute-subacute phase, we metamorphose acute DWI lesion

to subacute DWI lesion. During subacute-final phase we deform the latter into final T2-w

lesion. We estimate the deformation maps for both phases of DWI lesion evolution (images

under the black arrows). The red arrows point to highly expanding (red) areas and blue

arrows point to highly contracting (blue) areas.

Figure 2. Distribution of rMTT perfusion values (x-axis, ratio, therefore no unit) and the

DWI lesion mean deformation magnitude (y-axis mm/4 hours) between the acute and

subacute images for one patient. Blue dots are rMTT values in expanding areas of the DWI

lesion and pink dots are rMTT values in contracting areas of the DWI lesion. The peak of the

fitted Gaussian curve (grey line) represents the rMTT value associated with the maximum

mean contraction magnitude. The black arrows point to two perfusion thresholds on the grey

curve: p1 representing the peak of the Gaussian curve minus its standard deviation and p2 the

Gaussian peak plus its standard deviation. The perfusion confidence interval from p1 to p2

defines a range for perfusion values associated with the most rapidly contracting diffusion

areas. Same parameters are estimated from the red line fitting the pink dot distribution (for

expansion).

Figure 3. Acute rMTT values associated with rapidly deforming DWI lesion areas graphed

for all patients –ordered left to right by increasing admission NIHSS score (values on top of

the vertical bars). The centre dot = rMTT values associated with the maximum of DWI lesion

mean deformation magnitude (=peak of Gaussian curve in Fig 2). The limits of the vertical

blue and red bars represent the lower and the upper acute rMTT values (interval [p1, p2] in

Fig 2) associated with rapidly contracting (blue) vs. expanding (red) DWI lesion areas

between the acute and subacute timepoints.

Figure 4. Subacute rMTT values associated with rapidly deforming DWI lesion areas

graphed for all patients –ordered left to right by increasing admission NIHSS score (values on

top of the vertical bars). The centre dot = rMTT value associated with the maximum of DWI

lesion mean deformation magnitude. The limits of the vertical blue and red bars represent the

confidence interval (in Fig 2) associated with rapidly contracting (blue) vs. expanding (red)

DWI lesion areas between the subacute and final timepoints.

Figure 5. Acute rMTT values associated with rapidly deforming DWI lesion areas graphed

for STIR patients – ordered left to right by increasing admission NIHSS score (values on top

of the vertical bars). The centre dot = rMTT values associated with the maximum of DWI

lesion mean deformation magnitude (=peak of Gaussian curve in Fig 2). The limits of the

vertical blue and red bars represent the lower and the upper acute rMTT values (interval [p1,

p2] in Fig 2) associated with rapidly contracting (blue) vs. expanding (red) DWI lesion areas

between the acute and subacute timepoints.

Table 1. For contraction and expansion rMTT maxima, each column successively shows

their min, max and mean±standard deviation values across patients in two different datasets.

For DWI lesion volumetric proportion of highly dynamic areas, we show the min, max and

median values.

Derivation dataSTIR data

Acute-subacute phase†

Subacute-final phase†

Acute-subacute phase

Contraction rMTT value

MinMax

mean±SD

0.12.17

0.74±0.63

0.852.12

1.36±0.47

0.912.72

1.34±0.55

Expansion rMTT value

MinMax

Mean±SD

0.13.18

0.8±0.82

0.732.02

1.33±0.41

0.82.94

1.32±0.32

DWI lesion volumetric proportion of highly contracting areas* (%)

MinMax

Median

0.289.093.39

0.337.983.25

013.084.16

DWI lesion volumetric proportion of highly expanding areas* (%)

MinMax

Median

0.3612.614.38

0.4214.953.69

08.731.81

* Highly contracting areas are voxe0003ls within the DWI lesion boundary whose speed of

contraction is higher than the mean of the speed of contraction within the DWI lesion minus

its standard deviation. Highly expanding areas are voxels of the DWI lesion whose speed of

expansion is higher than the mean of the speed of contraction of the DWI lesion plus its

standard deviation.

† Acute-subacute phase defines the metamorphosis of acute DWI lesion into subacute DWI

lesion and subacute-final phase defines the metamorphosis of the latter into final T2-w at

≥1month.